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Published online: 2010-11-24
Urcohomologies and cohomologies of N-complexesNaoya Hiramatsu and Goro C. Kato (1) Okayama University, Japan
(2) California Polytechnic State University, San Luis Obispo, USA
For a general sequence of objects and morphisms, we construct two N-complexes. Then we can define cohomologies (i, k)-type of the N-complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of N-complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of N-complexes are given.
Keywords: N-complex, N-exactness, complexifying functor, urcohomology
Hiramatsu Naoya, Kato Goro: Urcohomologies and cohomologies of N-complexes. Port. Math. 67 (2010), 511-524. doi: 10.4171/PM/1875